1. Field of the Invention
The disclosed subject matter relates generally to well log interpretation. More specifically, this invention relates to using combinations of well logging measurements to derive reservoir fluid volumes and rock properties.
2. Background Art
One type of tool used for investigating a formation around a borehole is a nuclear magnetic resonance (“NMR”) logging tool. NMR tools are well known in the art. They measure the relaxation rates of hydrogen atoms in the pore spaces of earth formations by detecting the amplitude and decay rate of signals resulting from pulsed NMR spin-echo sequences. The NMR tool emits a sequence of radio-frequency pulses into the formation and then monitors the returning pulses, which are called “spin-echoes.” The amplitude of the spin-echoes measured by the NMR tool are proportional to the mean density of hydrogen nuclei in the fluid that occupies the pore spaces in the NMR tool's volume of investigation. Because the hydrogen densities in water and in liquid hydrocarbons are approximately the same, the detected NMR signal is proportional to the volume fraction of liquid occupying the pore space. One such NMR tool is described in U.S. Pat. No. 6,147,489 to Freedman et al.
In gas-bearing formations, NMR derived formation porosity is too low because of the low hydrogen index of gas compared to that of water. Similarly in reservoirs containing very viscous or heavy oil the NMR derived porosity is too low. The porosity deficit is caused by the very short relaxation times in heavy oils. That is, the signals decay so fast that significant signal amplitude is lost before the first spin-echo is detected. In formations that do not contain gas or very viscous oil, the NMR signal is related to the total porosity of the formation. The porosity determined by the NMR measurement is governed by:φnmr=φ0(H0P0−HwPw)+φHwPw  (1)where φnmr is the measured NMR porosity, φ0 is the oil filled porosity, φ is the total rock porosity, Pw and P0 are polarization functions for water and oil, and Hw, and H0 are the hydrogen indices of water and oil.
As is known in the art, the polarization function accounts for the degree of magnetization that is achieved during the wait time (W) that precedes each measurement. The measurable magnetization depends on the longitudinal relaxation time (T1) of the fluid and W. By selecting a sufficiently long wait time between experiments, the polarization functions can be made to approach 1 (i.e., Pw≅Po≅1). Because it is often true in practice that the hydrogen indices of water and oil are about one (i.e. Hw≅Ho≅1), Equation 1 reduces to:φnmr≅φ  (2)Thus, the total NMR porosity measured by an NMR tool in an oil-bearing formation is typically close to the formation porosity.
Another tool used for investigating a formation traversed by a borehole is a microwave or high-frequency dielectric tool. Often called electromagnetic propagation tools, dielectric tools are well known in the art. Microwave or high-frequency dielectric measurements have been used since the late 1970s to provide estimates of the fluid saturations in the flushed zone adjacent to a borehole drilled into an earth formation. A typical electromagnetic propagation tool has transmitters and receivers located on a pad placed in contact with the borehole wall. The transmitters transmit microwaves or high-frequency electromagnetic radiation into the formation penetrated by the borehole. The receivers, located in at least one additional location on the pad, measure the phase shift and attenuations of the radiation as it propagates through the formation. The phase shift and attenuation measurements can be inverted using models to obtain formation travel times tpl, and attenuations At, of the electromagnetic fields propagating in the formation (Freedman and Vogiatzis, Geophysics 44, no. 10, 969–986, 1979). The travel times for some minerals and fluids commonly found in earth formations are shown in Table 1. (Schlumberger Log Interpretation Principles, 1987, p. 126).
Mineral or FluidTravel Time (ns/m)Sandstone7.2Dolomite8.7Limestone 9.1–10.2Anhydrite8.4Halite7.9–8.4Gypsum6.8Shale7.45–16.6Oil4.7–5.2Gas3.3Water25–30Because the dielectric constant of water is much higher than the dielectric constants of hydrocarbons and the formation matrix material, the measured travel time is mostly dependent on the fraction of water in the formation.
The measured formation travel times can be related via a theoretical equation:{tilde over (t)}pl={tilde over (t)}pwφ−φ0(tpw−tpo)  (3)where {tilde over (t)}pl=tpl−tpma, {tilde over (t)}pw=tpw−tpma, tpl is the travel time measured by the tool, tpw is the brine travel time. The brine travel time is a function of temperature (T) and salinity (s), tpma is the travel time of the rock matrix, tpo is the travel time of the crude oil, φ is the total formation porosity, and φ0 is the oil-filled porosity. The travel times are the inverse phase velocities of electromagnetic wave propagation in the respective media. Equation 3 represents a “dielectric mixing law” that relates the constituent travel times to the formation travel times. Other mixing laws can be derived that serve the same purpose.
Density logs are another type of wellbore measurement that are well known in the art. A density logging tool contains a radioactive source that emits medium-energy gamma ray radiation into the formation. The density logging tool also contains a detector at some distance away from the source. Due to Compton scattering with atomic electrons in the formation, the gamma rays lose energy as they propagate through the formation. The decrease in the gamma ray energy is related to the electron density in the formation, and, thus, is also generally related to the formation bulk density ρb. The bulk density can be related to the porosity of the formation by the following equation:ρb=φρf+(1−φ)ρma  (4)where ρf is the average density of the fluid in the pore spaces, ρma is the density of the rock matrix, and φ is the formation porosity.
The NMR, density, and dielectric measurements and equations discussed above are applicable to measurements made in earth formations by conventional logging tools. The conventional tools include wireline logging tools and logging while drilling (“LWD”) tools. For dielectric measurements of reservoir fluids in rocks, it is important to make high-frequency measurements in order to avoid complicated dispersion or frequency dependent effects that cloud the interpretation of low-frequency dielectric measurements in reservoir rocks.
The NMR, density, and dielectric measurements can also be performed on samples of bulk fluids withdrawn from the formation by a fluid sampling tool like the Schlumberger Modular Dynamics Tester (MDT) tool or similar tool. These tools are discussed in several recent patents (Kleinberg, U.S. Pat. No. 6,346,813 B; Prammer, U.S. Pat. No. 6,107,796; Edwards, et al., U.S. Pat. No. 6,111,409; Blades and Prammer, U.S. Pat. No. 6,111,408). A fluid sampling tool typically uses packers to isolate a portion of the borehole wall. The pressure within the packers is reduced until the formation fluid flows into the sampling tool. Another type of sampling tool uses a probe that is inserted into or pressed against the formation, and fluid is withdrawn. Usually, the formation fluid is monitored, with an optical device for example, until there is no change in the formation fluid flowing into the sampling tool. At that point, it is assumed that the formation fluid that is flowing into the sampling tool does not contain any mud or mud filtrate and is comprised substantially of native formation fluids.
The equations discussed above and in the following sections of this patent are valid for NMR, density, and dielectric measurements made on bulk fluids in a sample module or flow line of a tool like the MDT that can be equipped with NMR, density, and dielectric measuring sensors. The sensors can be placed in the flow line so that the measurements are made while the fluids are in motion. Alternatively, a fluid sample can be diverted to a measurement cell where the measurement can be made on the stationary fluid. For measurement of bulk fluid dielectric properties it is not necessary to operate at high frequencies because there is negligible dispersion in the dielectric properties at lower frequencies. The equations for bulk fluids measured outside the formation can be obtained from equations appropriate for rocks by simply setting the rock matrix parameters to zero. That is, for bulk fluids, ρma=0 and tpma=0 in the above equations.